A priori estimates for quasilinear degenerate parabolic equations

We prove some maximum and gradient estimates for classical solutions to a wide class of quasilinear degenerate parabolic equations, including first order ones. The proof is elementary and exploits the smallness of the domain in the time direction.

     

An experimental analysis of a population based approach for global optimization

In this paper we perform a computational analysis of a population based approach for global optimization, Population Basin Hopping (PBH), which was proven to be very efficient on very challenging global optimization problems by the authors (see ). The experimental analysis aims at understanding more deeply how the approach works and why it is successful on challenging problems.     

Mathematical and numerical analysis of a simplified time-dependent viscoelastic flow

A time-dependent model corresponding to an Oldroyd-B viscoelastic fluid is considered, the convective terms being disregarded. Global existence in time is proved in Banach spaces provided the data are small enough, using the implicit function theorem and a maximum regularity property for a three fields Stokes problem. A finite element discretization in space is then proposed. Existence of the numerical solution is proved for small data, so as a priori error estimates, using again an implicit function theorem. Supported by the Swiss National Science Foundation. Fellowship PBEL2–114311.     

Synthesis of potential selective cox‐2 enzyme inhibitors derived from ethyl ester of 2‐isothiocyanato‐5‐phenyl‐3‐thiophenecarboxylic acid

Derivatives containing the thieno[2,3‐d]pyrimidin‐4‐one system, potential selective COX‐2 inhibitors, were prepared starting from ethyl ester of 2‐isothiocyanato‐5‐phenyl‐3‐thiophenecarboxylic acid ( 2 ); their structural elucidation is also reported.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

Calabi's diastasis function for Hermitian symmetric spaces

In this paper we study the Calabi diastasis function of Hermitian symmetric spaces. This allows us to prove that if a complete Hermitian locally symmetric space (M,g) admits a Kähler immersion into a globally symmetric space (S,G) then it is globally symmetric and the immersion is injective. Moreover, if (S,G) is symmetric of a specified type (Euclidean, noncompact, compact), then (M,g) is of the same type. We also give a characterization of Hermitian globally symmetric spaces in terms of their diastasis function. Finally, we apply our analysis to study the balanced metrics, introduced by Donaldson, in the case of locally Hermitian symmetric spaces.     

Novel ethero atoms containing polyesters based on 2,6‐naphthalendicarboxylic acid: A comparative study with poly(butylene naphthalate)

Poly(butylene naphthalate) (PBN), poly(diethylene naphthalate) (PDEN), and poly(thiodiethylene naphthalate) (PTDEN) were synthesized and characterized in terms of chemical structure and molecular weight. The polyesters were examined by TGA, DSC, and DMTA. All the polymers showed a good thermal stability, even though depending on chemical structure. At room temperature they appeared as semicrystalline materials; the effect of the introduction along the PBN polymer chain of ether oxygen atoms or sulfur ones was a lowering in the T_g value, a decrement of T_m, and a decrease of the crystallization rate. Changing in chemical structure also affects the main α absorption associated with the glass transition which moves to lower temperature and whose energetic requirements decrease. The results were explained as due to the presence of highly flexible C? S? C or C? O? C bonds in the polymeric chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1694–1703, 2007     

Integer linear programming models for 2-staged two-dimensional Knapsack problems

 We are given a unique rectangular piece of stock material S, with height H and width W, and a list of m rectangular shapes to be cut from S. Each shape's type i (i = 1, ..., m) is characterized by a height , a width , a profit , and an upper bound ub _i indicating the maximum number of items of type i which can be cut. We refer to the Two-Dimensional Knapsack (TDK) as the problem of determining a cutting pattern of S maximizing the sum of the profits of the cut items. In particular, we consider the classical variant of TDK in which the maximum number of cuts allowed to obtain each item is fixed to 2, and we refer to this problem as 2-staged TDK (2TDK). For the 2TDK problem we present two new Integer Linear Programming models, we discuss their properties, and we compare them with other formulations in terms of the LP bound they provide. Finally, both models are computationally tested within a standard branch-and-bound framework on a large set of instances from the literature by reinforcing them with the addition of linear inequalities to eliminate symmetries. Received: October 17, 2000 / Accepted: December 19, 2001 Published online: September 27, 2002 Key words. packing – cutting – integer linear programming